The Stress-Dependent Random Walk
Posted: 8 Jan 2016
Date Written: November 20, 2015
A log-normal random walk with parameters that are functions of market stress naturally accounts for volatility clustering and fat-tailed return distributions. Fitting this model to a stock and a bond index we find no evidence of significant misspecification despite the fact that the model has no adjustable parameters. This model can be interpreted as a stochastic volatility model without latent variables. We obtain a closed-form expression for the Value at Risk (VaR) that accommodates returns of any magnitude and discuss several other applications.
Keywords: Market model, regime-switching, stochastic volatility, value at risk, market stress, lognormal random walk, volatility clustering, fat tails
JEL Classification: C22
Suggested Citation: Suggested Citation